A universal approach by Laplace transform to the variational iteration method for fractional derivatives with the nonsingular kernel is presented; in particular, the Caputo-Fabrizio fractional derivative and the Atangana-Baleanu fractional derivative with the non-singular kernel is considered. The analysis elaborated for both non-singular kernel derivatives is shown the necessity of considering...

in this paper, the solution of the evolutionaryfourth-order in space, sivashinsky equation is obtained by meansof homotopy perturbation method (textbf{hpm}). the results revealthat the method is very effective, convenient  and quite accurateto systems of nonlinear partial differential equations.

The motion of the shoreline in sedimentary ocean basin were investigated and solved using modified variational iteration method since it provides an efficient approximate solution problem under consideration, which appears to be accurate when consecutive error between iterative solutions is evaluated. A diffusion equation with specified beginning boundary conditions, a moving interface type ref...

The aim of this paper is to solve numerically the Cauchy problems nonlinear partial differential equation (PDE) in a modified variational iteration approach. standard method (VIM) first studied before modifying it using Adomian polynomials decomposing terms PDE attain new iterative scheme (MVIM). VIM was used iteratively determine parabolic obtain some results. Also, PDEs with aid Maple 18 soft...

This paper features a survey of some recent developments in techniques for obtaining approximate analytical solutions of some nonlinear differential equations arising in various fields of science and engineering. Adomian’s decomposition method is applied to some nonlinear problems, and some mathematical tools such as He’s homotopy perturbation method and variational iteration method are introdu...

This paper presents using a new modified homotopy perturbation method (NHPM) for solving linear and nonlinear systems of differential-algebraic equations (DAEs) of index one or higher index without index reduction. By using this scheme, explicit exact solution is calculated in the form of a convergent power series with easily computable components. Some examples are given to illustrate the simp...